berger



July 5, 1932. H. L. BERGER CALCULATING momma nucnusm Filed Aug 28. 1929 attained:

[Pat nted ltllyis, 1932.

may 1,. man, or 433mm, LOUISIANA cucunume moms arraclmmr to Application filed August 28, 1929. Seriatlo. 889,038.

- This invention relates to an attachment for use upon a calculating machine and more particularly to a device adapted to be applied to an adding machine of a conventional construction in operative relation to windows or openings through which totals are disclosed and through the use of, which subtraction, 'multiplication, division, and other mathematical problems may be very n easily solved by use. of an adding machine of a conventional ty Another object o the invention is to so form the attachment that a main bar constituting part of the attachment maybe firmly secured across the upper wall of an adding machine and pointers adjusted longitudinally of the bar and secured in such position in which they extend toward selected total windows of the'adding machine.

Another object of the invention is to so mount the ointers that both may be moved longitudina y of'the bar at the same time or adjusted independently of each other.

Another object of the invention is to proat vide an attachment of this character wherein a strip above the main bar is held in proper position above the bar by clamps which carry the pointers. v

The invention is illustrated in the accomae panying drawing, wherein:

Figure 1 is a pers tive view of an adding machine wlth t e attachment appliedthereto.

Figure 2 is a view showing the attachment in front elevation and shown applied to the 1 casing of the adding machine.

Figure 3 is a top plan view of the attachment and illustrating its relation to the total windows of the addingmachine.

Figure 4 is a transverse sectional view taken on the line 4-4 of Figure 2.

Figure 5 is a similar view taken on the line 5-5 of Figure 2. I This improved attachmentyis adapted for use in connection with an adding machine of a conventional construction such as shown in Figure 1 of the drawing and indicated in general by the numeral 1. The machine ineludes the usual keyboard 2 and "o 5 handle 3 and has the upper wall 4 0 its casrating ing formed with the usual openings or windows 5 through which totals are disclosed.

The main bar 6 of this attachment is formed of metal and is of such length that it extends across the upper-wall of the adding machine for the full width thereof. Brackets 7 are riveted or otherwise firmly secured at the ends of the bar 6 in depending relation thereto and adjacent their lower ends are formed with threaded openings 8 so that when the attachment is in place with the brackets hearing against the side walls 9 of the addv ing machine casing, bolts 10 which are threaded through the openings 8, may have their reduced ends 11 engaged'in openings formed in the side walls of the adding machine casing and firmly holdthe attachment in position. It will thus be seen that the attachend'of the strip and the slot there has been formed a boss 14 and threaded opening or passage 15. Beneath the boss 14 a clamp 16 is riveted or otherwise firmly secured against the under face of the strip 12 and this clamp is formed with an opening 17 registering with the opening 15. Side portions of the clamp are extended downwardly to form arms 18 so that the clamp straddles the main bar 6, as shown clearly in Figure 5, and against the lower ends of the arms 18 is secured a' it may be easily turned until its lower end bears against the upper face of the bar and thereby exertslpressure to bind the clamp against the bar. Therefore, the clamp, together with the strip 12, may be shifted longitudinally of the main bar and secured in a set position with the pointer extending toward a selected total window of the adding machine.

A second clamp 23 which is also adjustable longitudinally of the main bar is disposed between the main bar and the strip 12. This clamp has depending arms 24 which extend the slot 13 in the strip 12 and upon the upper end of this stem is screwed a nut 28 which, when tightened, draws the clamp upwardly into binding engagement with the under surface of the strip 12 and causes the clamp to be firmly but releasably secured in a set position. It will thus be seen that the clamp 23 can be loosened and slid longitudinally of the bar and strip for adjustment of its pointer independently of the pointer 20 and that by releasing the set screw 21 the pointer 20, together with the strip 12 and pointer 26,- may be slid longitudinally of the main bar as a unit.

This attachment is applied to an adding machine of a conventional type and when the attachment is not in use the pointer 20 may be set opposite the-first total window at the right of t e machine and the pointer 26 at the last total window or both pointers may be shifted to a position at the right of the adding machine beyond the total windows. An

adding machine equipped with this attach ment may be employed to easily and quickly solve any mathematical problem and in the followingthere has been set forth preferred methods which will be followed when solving problems.

The examples illustrating this improved.

method of calculation are supposed to be worked on an adding machine of a capacity 3f 7 figures as shown by this row of seven ots:.......

Add't' '1 a h i Ion 1S necessam y passe by smce t e The minuend has 3 figures more than the subonly available short cut to it is to perform the operation on the machine in the usual way. Subtraction is instantly performed on any ordinary type of adding machine. In this unique way of subtracting the difference between any of the 10 numerals and 9 is called its complement: For instance, the difference between 4 and 9 being 5 it follows that 5 is the complement of 4, and inversely 4 is the complement of 5. Thus considering any number as, for example, 738, the complements of its figures are consecutively 2, 6 and 1, hence 261 is the complement of 738. i

The new method of subtraction being based are 8 and add it "to its unit figure 7 by numbers are the consecutive multiples of 9,

and either one of the two figures of any of these multiples is the complement of the other, for instance, in 27, 2 is the complement of 7 and vise versa. Therefore it is obvious that 1 these5 numbers can be readily remembered, and, in fact, a short practice will be sufiicient to bring about result so that, by merely glancing at a figure, as, for example, 6, it will recall at once the multiple 36, and thus the complement 3 will be instantly present in the mind and this will insure a rapidity in performing subtraction that cannot be had in any other way. In the examples illustrating use of the system, the clamp 23 and pointer 26 carried thereby have been designated pointer A and the clamp 16 and its pointer 20 referred to as pointer B.

EwampZe:-From 9547 subtract4719. In this case, both numbers have the same number of figures. If 1 is added to the initial figure 4 of subtrahend it makes 5, and 5 deducted from the initial figure 9 of minuend leaves 4, so, by glancing over the two numbers, it is seen at once that the remaining minuend is 4547, while the remaining sublonthemachine ...4548

Then add 280 complement of The answer being the total 4 8 2 8 Eaaample:From 8627 subtract 483. The minuend has one figure more thanthe subtrahend hence deduct 1 from its initial figregistering 7 6 2 8 Then add 516 complement of 483 1. 5 1 6 Answer .8 1 44 v 116 Ewamplm-From 170634 subtract 908.

trahend. These 3 figures make up the part 170-hence deduct 1 from 170 and add it to part 634 by registering-169635 on the machine 1 6 9 6 3 '5 Then add 91 complementof 908 Answer To subtract directly from a number in the machine. Suppose the following number in the machine. 2 9 6 3 7 and that 248 is to'be subtracted from it (a) 248 having 3 figures 100 'trahend is 719. Therefore, register 4547 plus A add 1- 2 9 6 3 8 (6) add 751 complement of ..'..751 c enre 'ter9inevery place in tile machine from 1 pointerAtothe left thus 99 9 9- and the answer will be the f 3 total .2 9389 Combined addition and subtraction In business calculations it is often neoes sary to add severalnumbers and to subtract the sum of them from another. The following example will show how this can be done in one operation. Suppose that you have a balance in the bank to your credit of $57 3.87 and the following checks were drawn against it: $4.90$27. 65$23.16$138.47- and that you want to know what tl16 1'18W balance is after the amounts of these checks have been deducted. As the original balance of $573.87 is a fivefigure number, each check item complement to be added must be also represented by the same number of figures therefore register 57387 and set pointer A on the machine next to its'initial figure 5 thus 57 3 8 7 Then add successively each check item complement, thusi V Complementof' 490or00490- 9 9 5 6 9 v Complementof 2765or02765- 9 7 2 3 4 Complementof 23160r02316 9 7 6 8 3 Complementof13847 8 6 1 5 2 A Total. .437965 Note that the figure 4 shown at the left of the total by the pointer A tallies with the numbers of check items registered. This is an effective way to check the work for ascertaining that no item has been overlooked in the addition. Now cancel this figure 4 byadding 96 to it, and at the same time add it to the A total .4379 65 Thus 96....4

Result 3 7 9 6 This result shows that the new balance is $379.69.

Multiplication In using the improved system of multiplication, it is, of course, necessary to be familiar tancy or'thought.

themultiplication table, also to know instantly thp sumof any two figures below 10 and to be able to-mentally add at once a single figure to a two-figure number, as, for

instanoa,"7 to 45-or 8 to 56. The sums of such combinations should be known the instant they are seen without the slightest hesi- This taken sider themental multiplication of a twofigure number by a single figure.

For example, in multiplying 78 by 4, the

' two partial products of 8 x 4or 32 units and of 7 x 4or 28 tens are clearly seen in the minds eye at a glance, and by mentally adding at once the 3 tens of 32 to 28 the product 312 of 78 x 4 is thus instantly formed and simultaneously registered on the machine.

blow in multiplying a three-figure number by a single figure, as, for instance, 836 by 7 since in 836 we have 8 hundreds and 36 units the product of 36 x 7 is registered as units thus 2 5 2 Then the product of 8 x 7 is y added as hundreds 5 6 The product of 836 x 7 being the total 5 8 5 2 In the two following Examples (a) and (b) and all subsequent multiplications use should be made of the pointer system AB toprevent any possibility of misplacing your figures, especially when figuring out and adding these products to numbers already registered on the machine.

To multiply a three-figure number by another of two figures. Example (0;) 457 Set double pointer AB to include 3 figures with pointer B opposite the first or unit Aplarfi on the machine thus Then multiply 457 by 8. By registering product of for granted, we will con- A B 57 x Sfrom pointer B .4 5 6 and product of 4 x 8 from pointer A 3 2 Total f 3 6 5 6 Now shift double pointer to bring pointer B to the tens .figure 5 of this first total A B thu's s 3 6 5 6 and multiply 457 by 6 By registering product of 57 x 6 from pointer B 3 4 2 and product of 4 x 6 from pointerA .'.24...

Answe 3 1 0 7 6 To multiply two numbers of three figures. Example (79) 573 Proceed asin foregoing example in multiplying 573 by 8, and then by 4 and till: rels3ult shown on the machine will be- 2 7 5 0 4 Shift double pointer to bring pointer B to the hundreds figure 5 of this total:

Now in performing long multiplications the following rules' must be observed:

Divisionwhen the divisor is a single figure.

EwampZe:-Divide 958 by 4.

Register the dividend thus 9 5 8 The divisor being a single figure set the double pointer AB to include 1+2, that is 3 figures, and 9 being the first part to be divided, shift the double pointer to bring pointer B to that A B figure, thus 9 5 8 9+4 is 2-1 (2 being the quotient and 1 the remainder) (11) add 2 to 9.to get remainder 1 1 1 (b) Cancel first 1 of 11 by adding 9 to it 1 1 (a) Add 1 to 1 at left to get A A B quotient 2 2 1 5 8 Shift double pointer to in- A B elude next figure 5 I 2 1 5 8 15+4 is s- 3 ((1) add 8 to 5 to get remainder 3 2 3 (b) cancel 2 byadding 8 to it 1 3 (0) add 2 to 1 to getquotient3 ..23.38 Shift the double pointer to A' B include last figure8 2 3 3 8 38+4 is 92 (a) add 4 to 8 to get remainder 2 4 2 (b) cancel 4 by adding 6170 it I 1 2 (0) add 8 to 1 to get quotient 9 2 3 9 2 Answer z+Quotient 239remainder 2.

Lightning method {601- computing lumber.In estimatinglum rthe board foot unit is 12, a number with which we are especially familiar, and its multiples below 100 are generally wellknown so that, with little practice,

any one can learn very soon to tell offhand how many times 12 is contained in any twofigure number. For instance, it will be an easy matter to tell at a glance that 38 is 3 times 12plus 2 or that 64 is 5 times 12- plus 4and to briefly express the same by merely saying that 38 is 3-2, meaning 3 twelves-plus 2 l 64 is 5-4 etc. and also that 100 is 84 200 is 16-8 300 is 2412 or 25 twelves and so on.

E'w'ampZw-How many square feet are there in 38 pieces each. 14 feet long of 2 by 4 inches scantling? Set pointer A on the machine to A the third place thus 2 4=8 and since 14=2 7 it follows that 2 times (728) or (94). This preliminary figuring being easily done mentally at a glance. Now register product of 38X 9 from pointer Athus:- 3 4 2 Product of 38 4is 152-01 100-F52 100 is (8-4) -add 8 to 342 and registei 4 as units ..350.4 52 is (44)-add 4 to.350- A and4to4 s54.s Answer :-354% sq. ft.

. Example ."-How many square feet are there in 26 pieces, each 18 feet long, of 2 x 8" lumber 2 2 8=16or (1-4) and since 18=2 9 it follows that 2 times (1-4) is (2- -8) -and9 times (2-8) is (1872) or 24 twelves. A

Hence re 'ster 24 thus i; 2 4 and multip y 26 by 24 from The same method can be applied in performing similar operations in which 12 is the main factor, for example, in figuring out p f .8 is 16 or (1--4)-.and 7 times (14) is izo the cost of 7 eggs at 42 cents a dozen42 is 3-6) and 7 times (3-6) is (2142) or 246) -answer :-24 cents.

Having thus described the invention, I claim:

1. A calculating machine attachment comprising a bar ada ted to be secured across a calculating machine adjacent and substantially parallel to total windows thereof, a

lo strip extendin parallel to said bar, a clamp carried by sai strip for releasably securing the strip in an adjusted position longitudinally of said bar and including a pointer projecting from a side of the bar to extend towards a selected total window of the calculating machine, and a second clamp adjustable longitudinally of the strip and bar and having a pointer projecting from the said side of the .bar. x

2. A calculating machine attachment comprising a bar adapted to be secured across a calculating machine adjacent and substantially arallel to total windows thereof, a strip exten 'ng longitudinally above said bar, a clamp carried by said strip for releasably securin the strip in an adjusted position longitu inally of said bar and including a pointer projecting from a side of the bar to extend towards aselected total window of the calculating machine, and a second clamp adjustable longitudinally upon said strip and including a pointer rojecting from the said side of the bar and a apted to be spaced'from the first pointer to a determined distance by adjustment of its clamp upon the strip.

3. A calculating machine attachment comprising a bar adapted to be secured across a calculating machine adjacent and substantially parallel to total windows thereof, a strip extending longitudinally above said bar, a clamp carried by said strip and including a lower plate extending beneath said bar and projecting transversely therefrom to form a pointer and a set screw to bear against the u per face of the bar and exert pressure to bmd the bar against the plate and releasably secure the stn in a set position with the pointer extendin in determined relation to total windows 2 the calculating machine, a second clamp carried by said strip and adapted to be adjusted longitudinally thereof and secured in a set position, and a pointer carried by the second clamp and projecting transversely from the strip and bar.

4. A calculating machine attachment comprising a bar ada ted to be secured across a calculating machine adjacent andv substantially parallel to total windows thereof, a stri extending longitudinally above said bar,

a 0 am adjacent one end of said strip to 'releasa 1y secure the strip in a set position and including a pointer projecting transversely from the strip and bar, and a second clam adjustable longitudinally of the strip and er and including a pointer projecting from the strip and bar and adapted to be spaced a determined distance from the first pointer by shifting its clamp longitudinally of, the strip and bar. 7

5. A calculating machine attachment com prising a barada ted to be secured across a calculating machlne adjacent and substantially parallel to total windows thereof, a

passage to bear against the bar and releasably secure the strip in a set position, a threaded stem extending upwardly from the other clamp body through the slot in said strip, and a nut upon said stem to bear against the strip and secure the clamp body in a set position with its pointer spaced from the pointer of the other clamp a determined distance.

In testimonywhereof I aflix my signature.

HENRY L. BERGER. [L. s.] 

